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Given f (2x + 1) = 8x + 74x2 + 4x + 2, find the range of F (x)
∵ f (2x + 1) = 8x + 74x2 + 4x + 2, ∵ f (2x + 1) = 4 (2x + 1) + 3 (2x + 1) 2 + 1, that is, f (x) = 4x + 3x2 + 1, Let f '(x) = - 2 (x + 2) (2x-1) (x2 + 1) 2 = 0, the solution is x = - 2 or 12, when x ∈ (- ∞, - 2), f' (x) = - 2 (x + 2) (2x-1) (x2 + 1) 2 < 0, when x ∈ (- 2, 12), f '(x) = - 2 (x + 2) (2x -
Given the function f (x) = x & # 178; (AX + 1) defined on R, where a is a constant. If x = 1 is an extreme point of function y = FX, find the value of A. if y = FX is an increasing function on interval (0,2), find the value range of real number a
1. Derivative = 3ax ^ 2 + 2x is 0 at x = 1, so 3A + 2 = 0, a = - 2 / 3
2. Derivative = 3ax ^ 2 + 2x = x (3ax + 2), if a = 0, the problem is satisfied; if a is not 0, then the two are (0,, - 2 / 3a), and there is no intersection between (0.2) and this interval, so - 2 / 3A0
In general, a > = 0
The domain of two different functions f (x) = x2 + ax + 1 and G (x) = x2 + X + a (a is a constant) is R. if the range of F (x) and G (x) is the same, then a=___ I really can't understand the same range!
F (x) = x ^ 2 + ax + 1 = (x + A / 2) ^ 2 - A ^ 2 / 4 + 1 > = - A ^ 2 / 4 + 1g (x) = x ^ 2 + X + a = (x + 1 / 2) ^ 2 - 1 / 4 + 1 > = - 1 / 4 + A to make their ranges the same, then - A ^ 2 / 4 + 1 = - 1 / 4 + a = = > A = 1 or - 5 can be simply understood as the value range of Y
RELATED INFORMATIONS
- 1. The following function, which is an increasing function in the interval (0, + ∞), is () A. y=ln（x+2）B. y＝−x+1C. y＝(12)xD. y＝x+1x
- 2. The monotone increasing interval of function y = x-ln (5 + x ^ 2) is_____ . The answer is (- ∞, + ∞) How to calculate? If you take the derivative of Y, you should get - 2x / (5 + x ^ 2), so that the derivative is greater than 0, and you get X
- 3. If the function f (x) = x & # 178; + A / x increases in the interval [2,3], then the value range of constant a It's a process
- 4. The known function f (x) = x & # 178; + A / X (x ≠ 0), (constant a ∈ R) (1) If f (x) is an even function, find a (2) When the constant a ≤ 16, we prove that the function f (x) increases monotonically on [2, + ∞)
- 5. Given that f (x) = 2 / (3 ^ X - 1) + m is an odd function, find the value of the constant M Given that f (x) = 2 / (3 ^ X - 1) + m is an odd function, find the value of the constant M It's the X of three, minus one
- 6. If the square of (x + y) is 7 and the square of (X-Y) is 5, find the value of XY Given the square of X - 2x = 2, find the square of (x-1) + (x + 3) (x-3) + (x-3) (x-1)
- 7. Given x + y = 5, x ^ 2 + y ^ 2 = 7, find the value of XY. Given x + y = 4, xy = 3, find the value of x ^ 2 + y ^ 2
- 8. Given x = 1 / √ 7 - √ 5, y = 1 / √ 7 + √ 5, find the value of x ^ 2 + XY + y ^ 2
- 9. If | x + Y-5 | + (xy-6) ^ 2 = 0, then x ^ 2 + y ^ 2=
- 10. The 96th power of 2 minus 1 can be divided by two integers between 60 and 70
- 11. 1. Given that f (x + 2) = 4x ^ 2 + 4x + 3 (x belongs to R), then the range of function f (x) is]
- 12. Given the function f (x) = √ 3sin (2x + φ), if f (a) = √ 3, then the relationship between F (a + 5 π / 6) and f (a + π / 12) is?
- 13. Given the function f (x) = 3sin (KX / 5 + π / 3), where k ≠ 0, find the maximum value of the function
- 14. 1: Given that the maximum value of F (x) = a-bcosx is 5 / 2 and the minimum value is negative 1 / 2, we can find the maximum value and the minimum positive period of G (x) = - 4A sinbx 2: Given that sin (a + π) = 3 / 5 and Sina × cosa < 0, the value of {2Sin (a - π) + 3tan (3 π - a)} / {4cos (A-3 π)} can be obtained
- 15. If 0 ≤ x ≤ 2, find the maximum and minimum values of the function y = 4 & nbsp; x-12-3 × 2x + 5 and the corresponding value of X
- 16. The domain of the function y = 1 / 1-tan2x is
- 17. Given that the range of F (x) = 2x ^ 2 + ax + B / x ^ 2 + 1 is [1,3], find the value of a and B
- 18. Find the range (1) y = cos & sup2; x-4sinx + 1
- 19. The minimum value of the function f (x) = the square of X + ax + 3 in [0,1] is
- 20. The maximum value of function y = - 2x + 1 in the interval [- 2,2] is the minimum value